Robust distortion risk measures

The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is crucial importance making well-informed decisions. In this paper, we quantify, for the class distortion with an absolutely continuous function, its distributional uncertainty by deriving largest (smallest) value when distribution has a known mean and variance and, furthermore, lies within ball—specified through Wasserstein distance—around reference distribution. We employ technique isotonic projections provide these complete characterization sharp bounds on their value, obtain quasi-explicit case Value-at-Risk Range-Value-at-Risk. extend our results account first two moments applications portfolio optimization model assessment.